The moduli space of two-convex embedded tori

Reto Buzano*, Robert Haslhofer, Or Hershkovits

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this short article, we investigate the topology of the moduli space of two-convex embedded tori Sn-1 × S1 R n+1 We prove that for n 3 this moduli space is path connected, and that for n 2 the connected components of the moduli space are in bijective correspondence with the knot classes associated to the embeddings. Our proof uses a variant of mean curvature flow with surgery developed in our earlier article 3 where neck regions are deformed to tiny strings instead of being cut out completely, an approach which preserves the global topology, embeddedness, as well as two-convexity.

Original languageAmerican English
Pages (from-to)392-406
Number of pages15
JournalInternational Mathematics Research Notices
Issue number2
StatePublished - 23 Jan 2019
Externally publishedYes

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© 2017.The Author(s).


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